A Flexible Automatic Lens Correction Procedure

Spencer, Gordon

doi:10.1364/ao.2.001257

Cited by 27 publications

(5 citation statements)

References 8 publications

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“…The least‐squares solution can be found once the following merit (error) function ξ is minimized: where F is a 2 S ‐element vector of the values f j , and F T denotes the transposed vector F . In the damped least‐squares technique, an optimization follows in repeating iterations (Spencer, 1963): where X 0 and X are the initial and the new vectors of the optimization parameters accordingly, A is the Jacobian matrix, i.e. a matrix of first partial derivatives of performance functions with respect to optimization parameters; p 2 is the damping factor; I is the unit diagonal matrix; F 0 is a vector of performance functions evaluated under initial parameters; and k l is the factor which defines the length of the descent vector.…”

Section: Optimization Algorithm For Reconstruction Of the Anterior Sumentioning

confidence: 99%

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Damped least‐squares approach for point‐source corneal topography

Sokurenko¹,

Molebny²

2009

Ophthalmic Physiologic Optic

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An optimization algorithm to be used in point-source corneal topographers is developed for the reconstruction of the topography of aspheric corneal surfaces. It is based on the damped least-squares technique. The reconstructions obtained with a topographer comprising 48 or 90 point sources for corneas having different forms (spherical, conicoidal, complex) and apical radii (5-16 mm) were simulated numerically. Zernike polynomials up to the seventh radial order were used for the description of the shape of the anterior corneal surface. With no noise, i.e. uncertainty in the position of the image of each object point, it is shown that this approach allows reconstruction of the surface with a root-mean-square (RMS) error of<5 x 10(-7) microm for the elevation map and 3 x 10(-7) diopter for the refraction map. With noise, to get an averaged surface elevation RMS error of <1 microm, or an averaged refraction RMS error of <0.25 diopter, each spot must be located (in the image plane) with an error <1 microm.

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Section: Optimization Algorithm For Reconstruction Of the Anterior Sumentioning

confidence: 99%

“…where F is a 2S-element vector of the values f j , and F T denotes the transposed vector F. In the damped leastsquares technique, an optimization follows in repeating iterations (Spencer, 1963):…”

Section: Optimization Algorithm For Reconstruction Of the Anterior Sumentioning

confidence: 99%

Damped least‐squares approach for point‐source corneal topography

Sokurenko¹,

Molebny²

2009

Ophthalmic Physiologic Optic

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“…We note that DLS optimization is fundamentally different than SGD in that it involves multidimensional loss functions and requires the computation of the Jacobian. In addition, DLS optimization offers the possibility of handling constraints through the mechanism of Lagrange multipliers, 12 which is not possible with SGD without resorting to penalty methods.…”

Section: Auxiliary Loss Based On Optical Performancementioning

confidence: 99%

Joint optical design for computer vision tasks: challenges and solutions

Côté,

Thibault,

Lalonde

et al. 2023

International Optical Design Conference 2023

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“…After that, numerous methods, including altering the additive damping in the DLS into multiplicative damping [31], were proposed to improve the convergence of the DLS. Except for the LS methods, Spencer [37] has specified that computers could only be regarded as a tool capable of offering optical designers temporary solutions because qualitative judgments and compromises were required in the optimization of optical systems. A novel concept of aberrations brought up by David S. Grey [38,39] is prominent, and this is principally due to the practical realization of his computer program, where a novel orthonormal theory of aberrations was applied in the optimization of optical systems.…”

Section: Overview Of Optical Imaging System Designmentioning

confidence: 99%

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

et al. 2022

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An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.

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A Flexible Automatic Lens Correction Procedure

Cited by 27 publications

References 8 publications

Damped least‐squares approach for point‐source corneal topography

Damped least‐squares approach for point‐source corneal topography

Joint optical design for computer vision tasks: challenges and solutions

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

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